The first of two appendices in There is a God by Antony Flew is a critique of the ‘New Atheism’ by co-author Roy Varghese. Varghese argues that there are some phenomena that are only explainable in terms of the existence of God (p. 161). His view is that atheism is a result of a deliberate refusal to look at the evidence, which is readily available in our immediate experience (p. 163). I think this goes hand in hand with Romans 1:20 which states, "For since the creation of the world God's invisible qualities--his eternal power and divine nature--have been clearly seen, being understood from what has been made, so that men are without excuse." In my experience powerful cases for both the existence and nonexistence of God can be made but it seems to me that it really boils down to how one interprets the evidence available.
I'm using this post as an introduction to five of the reasons why notable former atheist Antony Flew left atheism for deism. It is important to note that he did not become a christian theist, he simply looked at the available evidence and concluded that a superior mind is a more likely cause for why we have something rather than nothing, as opposed to naturalistic explanations. The following is a quick summary of Roy Varghese's work in There is a God and as I said I will go more in depth in each of the five points he makes later on.
First, Varghese argues that something had to always exist, either God or the universe (p. 165). He maintains that the theist argument is superior because the atheist says that the eternal existence of the universe is inherently unexplainable, but theists argue that the eternal existence of God is not inexplicable, just incomprehensible for humans (p. 165). The atheist view also fails to explain why something exists rather than nothing, and why the something that exists obeys the laws of nature (p. 171).
Second, Varghese contends that most of the ‘new atheists’ do not even address the origin of life. Only Dawkins attempts an explanation; he claims that ‘a chemical model need only predict that life will arise on one planet in a billion billion to give us a good and entirely satisfying explanation for the presence of life here’ (p. 173). Varghese criticizes this as ‘manifestly inadequate or worse’ (p. 172) and as ‘an audacious exercise in superstition’ (p. 173), and indeed not even such an inadequate model exists.
Third, atheists have to deal with consciousness. Although certain areas of the brain are associated with consciousness, they do not produce consciousness—a certain area of a person’s brain may show activity when thinking about a certain idea, but a neurologist cannot tell from that person’s MRI what he is thinking about. ‘Consciousness is correlated with certain regions of the brain, but when the same systems of neurons are present in the brain stem there is no “production” of consciousness’ (p. 174).
Fourth, ‘beyond consciousness, there is the phenomenon of thought, of understanding, seeing meaning’ (p. 176). ‘At the foundation of all of our thinking, communicating, and use of language is a miraculous power. It is the power of noting differences and similarities and of generalizing and universalizing—what the philosophers call concepts universals, and the like. It is natural to humans, unique, and simply mystifying’ (pp. 176–177). The brain plays a part in this process, but there is clearly a non-physical part to it, as well. Varghese argues that ‘they are the acts of a person who is inescapably both embodied and “ensouled”’ (p. 178).
Fifth, the atheists have to deal with the emergence of the self, which he calls ‘the most obvious and unassailable and the most lethal for all forms of physicalism’ (p. 181).
Most of this post was taken from: Review of There is a God
Keep in mind I do not believe any of these points are "proofs" of the existence of God. I just think that they are some examples of purely natural phenomenon (as opposed to supernatural) that can be interpreted as evidence for the existence of a "god."